材料热力学习题答案1

Theproblemsofthefirstlaw1.aleadbulletisfiredatafrigidsurface.Atwhatspeedmustittraveltomeltonimpact,ifitsinitialtemperatureis25℃andheatingoftherigidsurfaceoftherigidsurfaceisneglected?Themeltingpointofleadis327℃.Themolarheatoffusionoftheleadis4.8kJ/mol.ThemolarheatcapacityCPofleadmaybetakenas29.3J/(molK)(1.1)Solution:)/(5.112.20721]108.4)25327(3.29[2121)(2322smVvnnWQnMvmvWHTCnQQQabsorbmeltingpmeltincreaseabsorb2.whatistheaveragepowerproductioninwattsofapersonwhoburns2500kcaloffoodinaday?Estimatetheaverageadditionalpowderproductionof75Kgmanwhoisclimbingamountainatehrateof20m/min(1.2)Solution)/(24560208.975)/(12160602410467000//)(104670001868.4102500sin3SJthmgPSJtQtWPJQgincreaBurningBurning3Onecubicdecimeter(1dm3)ofwaterisbrokenintodropletshavingadiameterofonemicrometer(1um)at20℃.(1.3)(a)whatisthetotalareaofthedroplets?(b)Calculatetheminimumworkrequiredtoproducethedroplets.Assumethatthedropletsarerest(havezerovelocity)Waterhaveasurfacetensionof72.75dyn/cmat20℃(NOTES:thetermsurfaceenergy(ene/cm2)isalsousedforsurfacetensiondyn/cm)Solution)(25.218)106103(1075.72)(103)101(4)101(34)101(232523263631JSWmnSSSingletotal4.Gaseousheliumistobeusedtoquenchahotpieceofmetal.Theheliumisinstorageinaninsulatedtankwithavolumeof50Landatemperatureof25℃,thepressureis10atm.Assumethatheliumisanidealgas.(a)whenthevalveisopenedandthegasescapesintothequenchchamber(pressure=1atm),whatwillbethetemperatureofthefirstgastohitthespecimen?(b)Astheheliumflows,thepressureinthetankdrops.Whatwillbethetemperatureoftheheliumenteringthequenchchamberwhenthepressureinthetankhasfallento1atm?(1.4)Solution:)(180118298)(1185.229810101325501010101325)5500(1)()(118)101(298)()(0334.0/00KTTTKRRnCWTbKTPPTTAdiabaticapCRP5Anevacuated(P=0),insultedtankissurroundedbyaverylargevolume(assumeinfinitevolume)ofanidealgasatatemperatureT0.Thevalveonthetankisopenedandthesurroundinggasisallowedtoflowquicklyintothetankuntilthepressureinsidethetankisequalsthepressureoutside.Assumethatnoheatflowtakesplace.Whatisthefinaltempetureofthegasinthetank?Theheatcapacityofthegas,CpandCveachmaybeassumedtobeconstantoverthetemperaturerangspannedbytheexperiment.YouanswermaybeleftintermsofCpandCvhint:onewaytoapproachtheproblemistodefinethesystemasthegasendsupinthetank.(1.5)solution0/000/00)0()(TPPTTPPTTAdiabaticPPCRCR6.Calculatetheheatofreactionofmethanewithoxygenat298K,assumingthattheproductsofreactionareCO2andCH4(gas)[Thisheatofreactionisalsocalledthelowcalorificpowerofmethane]converttheanswerintounitesofBtu/1000SCFofmethane.SCFmeansstandardcubicfeet,takenat298and1atmNOTE:thisvalueisagoodapproximationforthelowcalorificpowderofnaturalgas(1.6)DATA:)()()(224gOHgCOgCHFOR80.5705.9489.17]/[0298molgKcalHsolution)1000/(9.2610252103048.01101076.191)/(76.191)89.1780.57205.94()2(22333332982982224422SCFBtumolgKcalHHHHHOHCOOCHCHOHCO7.Methaneisdeliveredat298Ktoaglassfactory,whichoperatesameltingfurnaceat1600K.Thefuelismixedwithaquantityofair,alsoat298K,whichis10%inexcessoftheamounttheoreticallyneededforcompletecombustion(airisapproximately21%O2and79%N2)(1.7)(a)Assumingcompletecombustion,whatisthecompositionofthefluegas(thegasfollowingcombustion)?(b)Whatisthetemperatureofthegas,assumingnoheatloss?(c)Thefurnaceprocesses2000kgofglasshourly,anditsheatlossestothesurroundingsaverage400000kJ/h.calculatethefuelconsumptionatSTP(inm3/h)assumingthatforgasH1600-H298=1200KJ/KG(d)Aheatexchangerisinstalledtotransfersomeofthesensibleheatofthefluegastothecombustionair.Calculatethedecreaseinfuelconsumptionifthecombustionairisheatedto800KDATASTPmeansT=298K,P=1atm22224ONOHCOCHfor2.82.89.117.1316)/(CmolcalCPSolution)(210448.1125.9100076.191298)/(25.9)]87.012.72(2.843.179.1171.87.13[01.0)(%87.0%%12.72%%43.17%2%%71.8)11.1(221791.1231%22)(0,,222222224KTTTCmolcalXCCbONCOOHCOOHCOOCHaiippp)/(1644)0224.011868.448.11)8001600(48.1125.9189570(102800000)/(189570)298800)](48.1187.8)48.1125.9[(100076.191)()/(87.848.11/]211002.22.816[)()/(3214)0224.011868.448.11)2981600(48.1125.9100076.191(102800000)/(280000040000020001200)(33min,,,,298,,33minhmVmolgcaldTnCnCHHCmolcalXCCdhmVhKJPCgConsuiirpiippiiprpgConsu8.Inaninvestigationofthethermodynamicpropertiesofa-manganese,thefollowingheatcontentsweredetermined:H700-H298=12113J/(gatom)H1000-H298=22803J/(gatom)FindasuitableequationforHT-H298andalsoforCPasafunctionoftemperatureintheform(a+bT)Assumethatnostructuretransformationtakesplaceinthegiventempeturerang.(1.8)Solution)298(0055.0)298(62.35011.062.35011.062.3522803)2981000(2)2981000(12113)298700(2)298700(]2[2229822222982TTHTCbababaTbaTbTdTadTCHTPTP9.Afuelgascontaining40%CO,10%CO2,andtherestN2(byvolume)isburntcompletelywithairinafurnace.Theincomingandongoingtemperaturesofthegasesinthefurnaceare773Kand1250K,respectively.Calculate(a)themaximumflametemperatureand(b)heatsuppliedtothefurnacepercu.ftofexhaustgas(1.9)molJHmol